The molecular weights determined by using colligative properties of substances which associate or dissociate will be abnormal and are called abnormal molecular weights. Ionic substances like NaCl, BaCl₂, AlCl₃, etc., ionize in solutions. Their colligative properties are high due to increase in number of particles when compared with solutions of non-electrolytes like glucose having equal molecular mass. When molecules of substance like acetic acid in benzene associate as dimers, trimers or polymers, the number of particles decreases and their colligative properties also decrease. The ratio of the observed colligative property and calculated colligative property is called Van’t Hoff factor i.

\[\text{i = }\frac{\text{observed colligative property}}{\text{calculated colligative property}}\]

\[\text{or, i = }\frac{\text{calculated molecular mass}}{\text{observed molecular mass}}\]

The value of Van’t Hoff factor i is greater than 1 for ionic substances while it has lower value than 1 for associated substances.

\[\frac{\text{calculated molecular mass}}{\text{observed molecular mass}} = \frac{\text{Normal number of solute particles}}{\text{Number of solute particles after dissociation or association}}\]

The molecular weight of sodium chloride determined by osmotic pressure method will be

lower than the theoretical value

The correct answer is option 3. lower than the theoretical value.

When a substance, like sodium chloride (NaCl), is dissolved in water, it undergoes dissociation into its constituent ions, Na⁺ and Cl⁻. This dissociation increases the number of particles in the solution compared to what would be expected based solely on the molecular weight of NaCl.

Osmotic pressure is a colligative property, meaning it depends on the number of solute particles in a solution, not on the identity of the solute particles. According to van't Hoff's law, the osmotic pressure (\( \pi \)) of a solution is directly proportional to the concentration of solute particles:

\(\pi = i \cdot M \cdot R \cdot T \)

Where:

\( \pi \) is the osmotic pressure,

\( i \) is the van't Hoff factor (the number of particles into which a solute dissociates in solution),

\( M \) is the molarity of the solution,

\( R \) is the ideal gas constant,

\( T \) is the temperature in Kelvin.

For a substance like NaCl, which dissociates into two ions (Na⁺ and Cl⁻) in solution, the van't Hoff factor (\( i \)) is 2. This means that for a given concentration of NaCl, the effective number of solute particles is twice the concentration of the substance.

So, when calculating the molecular weight of NaCl using osmotic pressure, the observed molecular weight will be lower than the theoretical value. Specifically, it will be half of the theoretical value because the osmotic pressure is proportional to the number of particles in solution.

This is why the molecular weight of sodium chloride determined by osmotic pressure method is lower than the theoretical value.